Deceleration of atoms in an n-photon process by means of a laser-travelling wave in the Dirac representation

A detailed theoretical study is made of the slowing down of the atomic beam by resonant laser radiation. By using the density matrix technique in the interaction representation, employing optical Bloch equations, one can obtain the average radiation force, with respect to the coherent state of the laser mode, represented in the complex plane. It is revealed that all the relevant variables are explicit functions of time via the average photon number. It is shown under the conditions which can be attained in practice that the behavior of the velocity and diffusion coefficients in both the longitudinal and transverse directions is consistent with previous works on such phenomenon.